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Chapter 11: Problem 1

What is a perfect square trinomial? Give an example.

Short Answer

Expert verified
A perfect square trinomial is a quadratic polynomial with three terms that can be factored into the square of a binomial. It takes the general form of \(a^2+2ab+b^2\) or \(a^2-2ab+b^2\). An example of a perfect square trinomial is \(x^2+6x+9\), which can be factored as \((x+3)^2\).

Step by step solution

01

Definition of Perfect Square Trinomial

A perfect square trinomial is a polynomial with three terms (quadratic) that can be factored as the square of a binomial. It takes the general form of \(a^2+2ab+b^2 \) or \( a^2-2ab+b^2\), where 'a' and 'b' are real numbers, integers, variables or a combination of these.
02

Factoring Perfect Square Trinomials

To factor a perfect square trinomial, you can identify the square root of the first term (a) and the square root of the last term (b). Once you have found these square roots, you can rewrite the trinomial as (a+b)^2 if the middle term is positive or as (a-b)^2 if the middle term is negative.
03

Example: Perfect Square Trinomial

Let's give an example of a perfect square trinomial: \(x^2+6x+9\) To factor this trinomial, we first identify the square root of the first term (x) and the square root of the last term (3). Since the middle term (6x) is positive, we rewrite the trinomial as a square binomial: \((x+3)^2\). Therefore, \(x^2+6x+9\) is an example of a perfect square trinomial.

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